Abstract
Statistical models are introduced for the simultaneous estimation of the changes of the b value and detection rate of earthquakes in a catalogue which develops in time or varies in space. The three characteristic parameters, including b, for the magnitude frequency distribution of detected earthquakes, are represented by respective three B-spline functions of time or location in a space. An objective Bayesian method is adopted for the optimal estimate of such functions with many unknown coefficients. The present procedure is applied to earthquake catalogues for Japanese seismic activity.